Halogenated cycloalkane compounds such as hexabromocyclododecane are commonly employed as flame retarding components in flame retardant treating agents used in flame retardant treating processes whereby fibers are imparted with a flame retardant property for maintenance of cleaning durability (durability against wet washing such as water washing, or dry cleaning). Also, Japanese Unexamined Patent Publication SHO No. 60-259674 discloses a flame retardant treating process employing as the flame retarding component a mixture of a halogenated cycloalkane compound such as hexabromocyclododecane with a phosphonate compound.